Second Order Effects of DNA Structure

On the previous page, we calculated the mean angle between base pairs to be around 32 degrees. In real life DNA there is a range from 20 degrees, less tightly wound DNA, to 50 degrees, more tightly wound DNA, with a mean of around 34 degrees. This is very close to the calculated number of 32 from the previous web page. Therefore we need to account for this variation in second order effects (Calladine, 1997; Stryer, 1995).

Also, the two bases of some base pairs are not coplanar. In reality they are twisted like the propellers of an airplane, hence the name propeller twisting (Stryer, 1995). The twist obviously changes the hydrogen bonds between the base pairs. This is not a problem because the Hydrogen bonds do allow for some distortion because they are somewhat weak bonds. Propeller twist is generally higher for A-T base pairs than for C-T base pairs by 5-7 degrees. The variations from the idealized structure allows for the bases to stack in such a way as to exclude more water (Calladine, 1997). These variations depend upon the base sequence. Proteins searching on a DNA strand can locate these sequences based upon the shape of the DNA molecule (Stryer, 1995). This is only one small example of how the shape of DNA effects biological functioning.
To represent the base pair interactions, Calladine has described a model used by the Swiss mathematician, Leonard Euler (1707-83). His theory states that if you have two rigid blocks, then you need six variables to describe their positions, three translations and three rotations. Translations move from side to side and up and down with out "turning" the object about. Rotations involve the turning of the object without moving it throughout the room. DNA only has three movements because the sugar phosphate backbone hinders complete movement of the DNA helices (Calladine, 1997).
The first variable is one of rotation and is called twist. This is the same twist we calculated to be 32 degrees (now we know this number varies) on the previous page. Calladine defines twist as, "it corresponds to a rotation about the local twist axis that runs vertically through, or near, the centers of any two neighboring base-pairs" (chapter 3).
The second variable of rotation is roll which is the rolling or opening of base pairs along the long axis of the base pair. In actuality the bases do not come apart much from one another (Calladine, 1997; Neidle, 1994). 
The final variable is one or translation called slide. The name explains the meaning quite well. Neighboring base pairs slide along the axis or direction of the DNA strand. There is little variation in slide because of the rigidity of the sugar phosphate backbones. The backbones allow for more flexibility in the roll and twist variations (Calladine, 1997; Neidle, 1994).
Clarification: The propeller twist is a property of single base pairs, not of two base pairs which lie over each other. Roll, twist and slide are properties of successive base pairs.

Until this point we have assumed only one structure of DNA. In reality there are three forms of DNA, A B and Z. We have only concentrated on the B form of DNA since this is the most common form found in nature.

A-DNA appears when the relative humidity is reduced below 75%. It is right handed as is B-DNA with antiparrallel strands and base pairs. However, A-DNA has tilted bases rather than normal to the helix axis. A-DNA is shorter and wider also (Stryer, 1995). 
Z-DNA is a hexanucleotide (CGCGCG) of antiparrallel strands with Watson and Crick base pairing. The unusual point of Z-DNA is that it is left handed in comparison to the right handedness of B-DNA. Additionally, the phosphates in the backbone are zigzagged. The zig-zag occurs because Z-DNA is a dinucleotide as opposed to a mononucleotide. The biological significance of Z-DNA is still unknown (Stryer, 1995).